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Value of c in Rolle's theorem for a given function

This type of question, asked 8 times: 3 May 2023 S2, 15 May 2023 S2, 11 May 2024 S1, 21 Apr 2025 S1, 13 Apr 2026 S2, 19 Apr 2026 S1, 20 Apr 2026 S2, 14 May 2026 S1. All 8 questions below, oldest first.

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  1. Question 1

    3 May 2023 S2

    142
    The value of cc for which Rolle's theorem for the function f(x)=x3−3x2+2xf(x)=x^{3}-3x^{2}+2x in the interval [0,2][0,2] are

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  2. Question 2

    15 May 2023 S2

    104
    The number of values of CC that satisfy the conclusion of Rolle's theorem in case of following function f(x)=sin⁡2πx, x∈[−1,1]f(x) = \sin 2\pi x,\, x \in [-1,1] is

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  3. Question 3

    11 May 2024 S1

    109
    Value of c satisfying the conditions and conclusions of Rolle's theorem for the function f(x)=xx+6,  x∈[−6,0]f(x) = x\sqrt{x+6},\; x \in [-6,0] is

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  4. Question 4

    21 Apr 2025 S1

    132
    If the function f(x)=x(x+3)e−x2f(x) =x(x+ 3)e^{-\frac{x}{2}} satisfies all the conditions of Rolle's theorem in [−3,0]\lbrack - 3,0\rbrack, then c is

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  5. Question 5

    13 Apr 2026 S2

    74
    If Rolle's theorem is applicable for the function f(x)=log⁡(x2+ax)f(x) = \log\left(\dfrac{x^2 + a}{x}\right) on [3,4][3, 4] with c∈(3,4)c \in (3, 4) such that f′(c)=0f'(c) = 0, then the value of f′′(c)f''(c) is

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  6. Question 6

    19 Apr 2026 S1

    77
    The value of cc satisfied by the Rolle's theorem for the function f(x)=x2(1−x)2,x∈[0,1]f(x) = x^2(1 - x)^2, x \in [0, 1] is...

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  7. Question 7

    20 Apr 2026 S2

    77
    The function f(x)=x(x+3)e−(12)xf(x) = x(x + 3)e^{-\left(\frac{1}{2}\right)x} satisfies all the conditions of Rolle's theorem in [−3,0][-3, 0], then c=c =

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  8. Question 8

    14 May 2026 S1

    75
    The value of cc for which the function f(x)=log⁡(x2+65x)f(x) = \log\left(\dfrac{x^2 + 6}{5x}\right) satisfies Rolle's theorem in the interval [2,3][2, 3] is ____

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